# i have trouble finding the answer to this and how to srt. there is a square and i havbe to find the area. HOweever inside the square is a triangle. the base of the triangle is 3 and the leg is 7. no height is given. plz help.

Is this a right triangle? Is the base or leg equal to a side length? Somehow, you have to relate the dimensions of the triangle to the square side. My suspicion is that it is a right triangle, and the height of the triangle is equal to a side of the square.

yes the base and the leg is to the side length. the height of the triangle is equal to the side of the square but no height is given so that is whyu i am confused on how to find the area of the square

Wouldn't the pythogrean theorm tell you the height?

hypotenuse^2= leg2^2 + leg1^2

solve for the unknown leg, which will be height.

## Yes, you're right! The Pythagorean theorem can be used to find the height of the triangle, which will also be equal to the side length of the square. Let's use the formula:

hypotenuse^2 = leg2^2 + leg1^2

In this case, the hypotenuse is the side length of the square, and the two other sides of the triangle are the given base (3) and leg (7). Substituting the values, we get:

s^2 = 3^2 + 7^2
s^2 = 9 + 49
s^2 = 58

Now, we can find the square root of both sides to get the value of s (the side length of the square and the height of the triangle):

s = √58

So, the side length of the square is √58, which is also the height of the triangle.

Now that we know the side length of the square, we can find the area of the square by squaring the side length:

Area of the square = side length^2
Area of the square = (√58)^2
Area of the square = 58

Therefore, the area of the square is 58 square units.